Magnetic fields are thought to play an important role in the formation of stars. However, that importance has been called into question by previous observations showing misalignment between protostellar outflows and magnetic fields, as well as inconsistency in field morphology from 10,000 -- 1,000 AU scales. To investigate these inconsistencies, we used the 1.3 mm full-Stokes polarimeter at CARMA to map dust polarization with ~2.5" resolution toward 29 star-forming cores and 8 high-mass star-forming regions as part of the TADPOL survey. We find that a subset of the sources have consistent magnetic field orientations between the large (~20") scales measured by single-dish submillimeter bolometers and the small scales measured by CARMA. Those same sources also tend to have higher fractional polarizations (measured by CARMA) than the sources with inconsistent large- to small-scale fields, presumably because there is less field twisting to reduce the polarization fraction. This suggests that at least in some sources, magnetic fields dominate turbulence over many orders of magnitude, from ~100 pc molecular cloud scales down to ~1000 AU protostellar envelope scales. However, even in the sources with consistent large-to-small-scale field orientations, the magnetic fields in the cores are misaligned with the disks and outflows in the central protostars -- a key result of the TADPOL survey. We also find that all sources exhibit the so-called "polarization hole" effect, where the polarization drops significantly near the total intensity peak. When this effect was seen in low-resolution single-dish maps, it was attributed to the averaging of unresolved structure in the plane of the sky. However, the higher resolution maps we present here resolve these twisted polarization morphologies, and yet the drop in fractional polarization persists, suggesting that fields are twisted along the line of sight, or that grain alignment is poor in dense regions with high extinction and high collision rates.